An optimal irrigation network with infinitely many branching points

DOI10.1051/cocv/2015028zbMath1343.49074arXiv1408.2406OpenAlexW2082053483MaRDI QIDQ2808058

Andrea Marchese, Annalisa Massaccesi

Publication date: 26 May 2016

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.2406

zbMATH Keywords

calibrationsbranching pointsGilbert-Steiner problemflat \(G\)-chainsirrigation network

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Calibrations and calibrated geometries (53C38)

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Cites Work

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• The Steiner problem for infinitely many points
• An equivalent path functional formulation of branched transportation problems
• Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity
• The regularity of optimal irrigation patterns
• Optimal transportation networks as flat chains
• Path functionals over Wasserstein spaces
• The Steiner tree problem revisited through rectifiable \(G\)-currents
• Optimal transportation networks. Models and theory
• Harmonic maps with defects
• A variational model of irrigation patterns
• Rectifiability of flat chains
• Interior regularity of optimal transport paths
• Existence and regularity results for the Steiner problem
• An example of an infinite Steiner tree connecting an uncountable set
• Are there infinite irrigation trees?
• Traffic plans
• Synchronic and Asynchronic Descriptions of Irrigation Problems
• Rectifiable and flat <i>G</i> chains in a metric space
• Optimal networks for mass transportation problems
• The formation of a tree leaf
• Optimal Design of Gas Pipeline Networks
• OPTIMAL PATHS RELATED TO TRANSPORT PROBLEMS
• Minimum Concave Cost Flows in Certain Networks
• Currents in metric spaces